A number machine is shown. Part a) Calculate the output when
the input is nine. Part b) Calculate the output when
the input is negative nine.
The number machine has two steps to
get from the input to the output, firstly subtracting one and secondly multiplying
by four. In part a), we’re told that the
input is nine. Subtracting one from nine gives us
an answer of eight. Multiplying eight by four is
32. This means that when the input is
nine, the output from the number machine is 32.
Part b) asks us to calculate the
output when the input is negative nine. Subtracting one from negative nine
gives us negative 10. Subtracting a number from a
negative number takes us further down our number line. We then need to multiply negative
10 by four. Multiplying a negative number by a
positive number gives us a negative answer. And 10 multiplied by four is equal
to 40. Therefore, negative 10 multiplied
by four is equal to negative 40. When the input to the number
machine is negative nine, then its output is negative 40.
Whilst we are not asked to in this
case, we could write the output 𝑦 as an expression in terms of the input 𝑥. The first step in our number
machine is to subtract one. Therefore, we would have 𝑥 minus
one. We then multiply this answer by
four, 𝑥 minus one multiplied by four. This is usually written with a four
in front of the bracket. So we have four multiplied by 𝑥
minus one. The output 𝑦 in this question is
equal to four multiplied by 𝑥 minus one. We could then use this to work out
the output when we are given any input 𝑥.